{"paper":{"title":"Minimal biquadratic energy of 5 particles on 2-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Tumanov","submitted_at":"2012-08-24T19:45:33Z","abstract_excerpt":"Consider n points on the unit 2-sphere. The potential of the interaction of two points is a function f(r) of the distance r between the points. The total energy E of n points is the sum of the pairwise energies. The question is how to place the points on the sphere to minimize the energy E. For the Coulomb potential f(r)=1/r, the problem goes back to Thomson (1904). The results for n < 5 are well known. We focus on the case n=5, which turns out to be difficult. In this case, the following results have been obtained. For n=5, Dragnev, Legg, and Townsend (2002) give a solution of the problem for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5044","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}